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Question

# Out of n students, a committee of 12 students is formed. If number of such committees containing 2 particular students A,B is 3 times the number of committees containing another 3 particular students D,E,F, then n is

A
32
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B
38
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C
45
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D
72
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Solution

## The correct option is A 32Out of n students, A,B are always included. Other 10 students from (n−2) students can be selected in n−2C10 ways. Similarly, the other committee can be formed in n−3C9 ways. Given that n−2C10=3×n−3C9 ⇒(n−2)!(n−12)! 10!=3×(n−3)!(n−12)! 9! ⇒n−210=3 ⇒n=32

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